MODERATE DEVIATIONS AND NONPARAMETRIC INFERENCE FOR MONOTONE FUNCTIONS

• 成果类型: Article
• 署名作者: Gao, Fuqing; Xiong, Jie; Zhao, Xingqiu
• 署名单位: Wuhan University; University of Macau; Hong Kong Polytechnic University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1583
• 发表日期: 2018
• 页码: 1225-1254
• 关键词: kernel density estimators; confidence-intervals; maximum; error; tests; MODEL

摘要

This paper considers self-normalized limits and moderate deviations of nonparametric maximum likelihood estimators for monotone functions. We obtain their self-normalized Cramer-type moderate deviations and limit distribution theorems for the nonparametric maximum likelihood estimator in the current status model and the Grenander-type estimator. As applications of the results, we present a new procedure to construct asymptotical confidence intervals and asymptotical rejection regions of hypothesis testing for monotone functions. The theoretical results can guarantee that the new test has the probability of type II error tending to 0 exponentially. Simulation studies also show that the new nonparametric test works well for the most commonly used parametric survival functions such as exponential and Weibull survival distributions.